Mahan defeated McIlroy 2-and-1 Sunday in winning the Accenture Match Play Championship in Arizona. It was his fourth PGA title.
It also puts him ninth in the rankings after starting the week ranked No. 22.
His move into the Top 10 shifts Phil Mickelson from ninth to 11th.
Also improving his position was Dustin Johnson, who goes from 10th to No. 7.
But McIlroy remains No. 2. He and world No. 3 Lee Westwood met in the match play semifinal, with both having a chance to take the No. 1 ranking with a win in the finals. Mahan got in the way, however, and Luke Donald is still on top of the rankings.
Donald, who has a ranking average of 9.131, has been No. 1 for 40 weeks. McIlroy's average is 8.598 and Westwood is at 8.170.
Johnson has an average of 5.111 and Adam Scott stays in eighth with 5.052, not far ahead of Mahan's 5.030, but Jason Day, down from eighth to 10th, is at 5.012.
The week's other major tour winner was John Huh, who outlasted Robert Allenby for a win after eight playoff holes at the Mayakoba Gold Classic Mexico. Huh, who started the year ranked 543rd, was 267th before the win and 137th after it.